Comments on "Broadband Matching Limitations for Higher Order Spherical Modes

Antenna Q and Stored Energy Expressed in the Fields, Currents, and Input Impedance

“…where ω 0 = (ω 1 + ω 2 )/2 and Γ 0 is the threshold of the reflection coefficient. Similarly, the Fano limit [22,[24][25][26] for a single resonance circuit, B ≤ 27.29/(Q|Γ 0, dB |), is an upper bound on the bandwidth after matching, where Γ 0, dB = 20 log 10 Γ 0 . For more general circuit networks, we consider the Q-values determined from the differentiated input impedance and the stored energy in equivalent circuit models, see also Fig.…”

“…We consider the Bode-Fano matching limitations [22,[24][25][26] for the cascaded shunt LC and series LC circuit in Fig. 3.…”

“…This is consistent with Q Z being a local function of the input impedance and Q ZB depending on the global (all spectrum) behavior of the input impedance. The bandwidth for a simple shunt and series resonance circuit [22] is also analyzed using matching networks and Fano matching bounds [22,[24][25][26] to illustrate a case with Q Z ≈ 0, where the inverse proportionality of the fractional bandwidth to Q fails for Q Z .…”

Bandwidth Limitations for Scattering of Higher Order Electromagnetic Spherical Waves With Implications for the Antenna Scattering Matrix

“…The computationally expensive numerical problem is solved by Villalobos et al in [38]. Alternatively, Kogan has shown that the solution can be found by solving a polynomial equation of order 2l + 1, see [24]. However, upper bounds on f ν (T [τ ] sml,sml ; k 0 a) can be derived by considering a single complex zero also for higher order waves, which gives a problem that is straightforward to solve numerically [29].…”

“…In form, the sum rules and limitations derived here are similar to those from optimal broadband matching of the spherical waves. Matching of ideal dipoles, the lowest order spherical waves, was considered by Hujanen et al [21], while higher order waves was treated by Villalobos et al [38], Nordebo et al [29], as well as Kogan (see [24] and references therein). One advantage that follows from the approach adopted in the present paper is that the shape and static material properties of the antenna are highlighted.…”